A "Sherlock-style forensic focus" is needed to finish Crossrail on time and within budget, an inquiry has found.
The route was due to open in December 2018 but has faced numerous delays.
A committee has urged Transport for London (TfL) to keep a "tight grasp" on the project's leadership and budget, which is now £18.6bn after a £825m boost of government cash in December.
TfL said there had been "many challenges", but the line would be opened "as soon as possible".
Known as the Elizabeth Line, the route, running from Reading to Essex through central London, has suffered from delays, budget complexities and issues with its construction work and signalling systems over the decade.
Management of the scheme was transferred from Crossrail Ltd to TfL, chaired by Mayor of London Sadiq Khan, in October 2020.
A cross-party London Assembly Transport Committee warned TfL and the mayor to ensure "past mistakes are not repeated".
It also said there may not be "enough resources or the right level of expertise" to complete its final phases with safety assurance activities and technical processes.
The inquiry noted the coronavirus pandemic had "exacerbated resource constraints" and created "possible staff burnout".
Chairwoman of the Transport Committee, Alison Moore, said it was "vital" TfL and the mayor "adopt a Sherlock-style forensic focus" to deliver the project on time and on budget.
She insisted Londoners "need assurance" that "they will be no further out of pocket".
"Covid-19 has understandably put increased financial and staff pressures on Crossrail opening the Elizabeth Line," she said.
"However there are aspects to delivering Crossrail, such as supporting employees' workloads and better forecasting project delays, that can contribute to delivering as promised."
She added it was "imperative" the line was "up and running as soon as possible".
London's transport commissioner Andy Byford said his focus "remains on safely opening the Elizabeth line as soon as possible".
"There have been many challenges with delivering the railway and I am confident lessons are being learned and applied in these complex final stages of delivery.
"The coronavirus pandemic has obviously had some impact on the project and ways of working, and Crossrail has responded to this by ensuring sites remain a safe place to work," he added.